Yeah, no. That’s not what you actually appear to be using, at least based on your post. The image you posted is of the Apple TV+ home page. The Apple TV+ logo on the upper right hand corner is the tell. Apple TV+ is a streaming service.
That’s a different thing than the “Apple TV (no +) App” that I linked to. If you click the link I posted and scroll down there appears is a graphic of what the Apple TV App looks like and there are 3 tabs at the bottom of that App — “Watch Now” Up “Library” & “Search” - tap Library and you’ll see what you’ve purchased from iTunes. Tap watch Now Natalie you’ll see offerings.
What you posted is not the Apple TV App. You should maybe try that.